Non-redundant random generation from weighted context-free languages

TL;DR

This paper introduces an efficient recursive algorithm for non-redundant random generation of multiple words from weighted context-free languages, outperforming rejection-based methods especially for large k.

Contribution

It proposes a novel recursive algorithm that enables non-redundant generation of words with significantly improved complexity over traditional rejection methods.

Findings

Recursive algorithm achieves O(kn log n) complexity after precomputation.

Rejection-based approach can have exponential time complexity in k.

Non-redundant generation cost is negligible compared to overall complexity.

Abstract

We address the non-redundant random generation of k words of length n from a context-free language. Additionally, we want to avoid a predefined set of words. We study the limits of a rejection-based approach, whose time complexity is shown to grow exponentially in k in some cases. We propose an alternative recursive algorithm, whose careful implementation allows for a non-redundant generation of k words of size n in O(kn log n) arithmetic operations after the precomputation of O(n) numbers. The overall complexity is therefore dominated by the generation of k words, and the non-redundancy comes at a negligible cost.